Flows induced by oscillations of a heated sphere

The flows induced by the translational linearly polarized vibrations of a heated sphere immersed in an incompressible fluid are studied. The fluid density does not depend on pressure and changes with temperature according to the linear law. The fluid is bounded by an immovable spherical envelope, and the system is subjected to the gravity field. The stream-function and temperature fields for creeping flow regimes are found analytically. The dependences of the characteristics of the non-linear convective regimes on the parameter values are obtained numerically using a finite difference method.